When preparing to drill a new well, the surveyed locations of any nearby wells are considered. As with most measurements, the survey measurements involve inaccuracies (survey uncertainty). While the new well is being drilled, the drill bit may not follow the planned path (drilling uncertainty). The potential for well collisions to occur is affected by survey uncertainty, the distance or interval between surveys (survey interval), drilling uncertainty, distance and intersection angle between the wells, and well diameter.
In view of survey uncertainty and drilling uncertainty, industry practice has been to design the path of a new well to be kept apart from any existing well at greater than a specified minimum distance in order to avoid well collisions. If, for economic or other reasons, the new well must be drilled closer to an existing well than this minimum distance, preventive actions, e.g., plugging the existing well, are taken to reduce the consequences of potential problems caused by well collision. Traditionally, this minimum distance is derived from experience and intuition, as a function of depth. While the traditional approach can be used to avoid well collisions, the approach does not always include rigorous risk assessments. This can lead to overly risky, and potentially dangerous, or overly conservative, and costly, drilling.
A better approach to avoid well collision problems is to mathematically assess the risk of well collision and the likelihood that a collision will result in a problem, and to develop appropriate action plans according to the assessed risk. For a problem to result from a well collision, wells have first to collide ("well collision probability") and then the collision has to lead to that problem ("event chain probability"). The probability for a well-collision related problem to occur is the product of the well collision probability and the event chain probability. The event chain probability depends on local conditions and may be determined by using conventional probability analysis techniques, such as event tree analysis, which are well known to those familiar with quantitative risk assessment (QRA). QRA is the development of a quantitative estimate of risk based on engineering evaluation and mathematical techniques. A primary challenge in developing QRA for well collision is to know how to estimate collision probability.
The need for a reliable method to estimate well collision probability has received attention from the upstream petroleum industry in recent years. In two papers published in 1990 and 1991, equations were proposed for straight holes (or portions of wells), and separate models for parallel and non-parallel holes were provided. (Thorogood, J. L., et. al: "Quantitative Risk Assessment of Subsurface Well Collisions," SPE Paper 20908, 1990; and Thorogood, J. L., Hogg, T. W. and Williamson, H. S. "Application of Risk Analysis Methods to Subsurface Well Collision," SPE Drilling Engineering, December 1991.) The model proposed in the papers for parallel wells is a two-dimensional (2-D) solution. While the papers indicate recognition of the need for a three-dimensional (3-D) solution for non-parallel wells and consider the effect of intersection angle between two wells, the papers do not propose a 3-D solution. The equations in the published papers appear to have the following shortcomings: (i) the calculated probability based on the equations can be much larger than 1.0 or 100%; (ii) the collision probability for non-parallel wells does not approach parallel wells when intersection angle approaches zero; and (iii) probability always decreases with increasing intersection angle, even for a short well segment.
Related U.S. Pat. Nos. 4,957,172 and 5,103,920 describe a system and method for drilling a second wellbore along a planned path with respect to a first wellbore. The patents are directed toward a method of drilling a relief well to intersect a blowout well at a target location in the blowout well for the purpose of relieving fluid pressure in the blowout well. The bases of the patents are maintaining high probabilities of find and of intercept, i.e., high probabilities that the blowout well can be located using a search tool in the borehole of the relief well and that the borehole of the relief well will intercept the blowout well at the target location, while maintaining a low probability of collision, i.e., a low probability that the borehole of the relief well will collide with the blowout well before the target location or that the borehole of the relief well will collide with another nearby well. The patents discuss use of a probable location distribution (PLD) and a relative probable location distribution (RPLD) for describing the locations of the borehole and the blowout well. The PLD is a quantitative description of where the well is located in statistical terms. The RPLD is a tri-axial location error distribution which includes the surface site errors and the systematic and random errors due to directional surveys of both the blowout and relief wells. The method of these patents uses probability equations based on errors in surveying but does not take into consideration other useful factors such as distance and intersection angle between the wells and well diameter.
Other work in this area has only marginally succeeded in developing a solution, albeit a 2-D solution, for calculating collision probability of two straight and parallel wells, a rare and unrealistic case. A common method to expand a 2-D solution for a 3-D problem is to sum or integrate the 2-D solution of many thin parallel slices of the 3-D space. This method has worked successfully in solving many engineering problems, e.g., stress analysis; but it is difficult to apply this thin-slice method directly for the well collision problem. The two small segments (thin slices) of the two near-by wells are constrained by their adjacent well segments. It is difficult to properly assign appropriate boundary conditions so that these two thin-slices may be considered as "free-body" for independent analysis. Consequently, calculating the collision probability of two wells by simply solving the 2-D problem of the thin slice and then summing them together generally will not provide usable results. The foregoing is true even for the case of two straight but non-parallel wells. The more likely case, where two wells are neither straight nor parallel, presents ever greater mathematical challenges. A truly 3-D solution is needed.